The course work at the California Institute of Integral Studies Transformative Studies Department is all really based around this idea of creative inquiry. The idea of creative inquiry does not mean just studying something in an interesting way, although I would guess that could be a portion of it. In my thinking about it, and from reading about it as educational style, it is more of a worldview that somebody takes on and thinks about their academic scholarship.
One of the professors in our program, Alfonso Montuori and my teacher for Introduction to Transformative Studies, seems like he is pretty prolific in writing about both creativity and creative inquiry. He describes there being two educational styles that are dominate in academia separate from the concept of creative inquiry. One of them is reproductive, in that they they are about the person who is learning reproducing others work verses creating their own work. This style also could be described as more coming from the head verses the hear. He describes the second style as a narcissistic style, where the learner is looking internally for their learning, he even goes as far as to say it is all navel gazing. This style could also be described as more from the heart.
The way this frame works in my head, is that there is a continuum that these two styles are on either side of. One looking at the head and one looking at the hear. Creative Inquiry would be right in the middle of the two.
I find the idea of creative inquiry pretty fascinating. I wrote an essay about it, that you could check out if you are interested The Ph.D. and Creative Inquiry: A Short Synthesis Paper.